(ii). We adapt the technique of [1]} to \(p\) -generalized
Gaussian smoothing. Let \(y=x+\mu \xi \) , then \(U_{\mu }(x)\)  is rewritten
in another form as
\(U_{\mu }(x) & =\mathrm {\mathbb {E}}_{\xi }[U(x+\mu \xi )]\\& =\frac{1}{\kappa \mu }\int _{\mathbb {R}^{d}}U(y)e^{-\frac{1}{p\mu ^{p}}\left\Vert y-x\right\Vert _{p}^{p}}dy.\) 
